Several DNA transposons are equipped with novel ways to control target site selection for insertion. A transposition target site selection phenomena exhibited by these transposons are referred to as transposition target immunity;DNA sites near a transposon end sequence are avoided as a target for additional insertion by the same kind of transposon. Phage Mu transposon is one such element and it uses an ATP-dependent DNA binding protein, MuB, as the central player in the target site selection to reduce the risk of self destructive insertion into its own genome. MuB ATPase controls each of the early steps of phage Mu DNA transposition: it assists transpososome assembly, it is involved in the target DNA site selection, it activates the MuA transposase for the strand transfer reaction, and it protects the transpososome from premature disassembly by ClpX chaperon protein until strand transfer is completed and the transposition intermediate is ready for DNA replication by the host replication proteins. In turn, the functional state of MuB is controlled by its ATPase cycle and by interaction with MuA. We have demonstrated that Mu transposition target selection involves establishment of a preferential distribution of the MuB ATPase along DNA molecules away from a Mu DNA sequence end to which MuA transposase binds. Techniques and instruments have been developed to study the structural and functional aspects of MuB-DNA complex at the single molecule level by using a sensitive fluorescence microscope/CCD camera system and also by electron microscopy. Using GFP-tagged MuB, assembly and disassembly of MuB polymers on single molecules of DNA immobilized on a slide glass surface were monitored under a variety of reaction conditions. We found that MuB forms polymers of heterogeneous sizes along the DNA and ATP-dependent assembly of MuB polymers involves stochastic DNA binding and nucleation events. Also, MuB dissociation takes place preferentially, but not exclusively, from the ends of a polymer and is tightly coupled to ATP hydrolysis. Finally, the MuA tetramer accelerates dissociation of MuB from DNA in a process dependent on a DNA-looping-mediated interaction of the MuB polymer and MuA tetramer. To explain the distance along the DNA that is influenced by target immunity, which exceeds the average passive DNA-looping distance, we measured the loop size distribution as a function of the time given for free DNA Brownian motion during which the looping interactions could take place. We demonstrated an increase of the average DNA loop size with the time of DNA Brownian motion, leading to a detailed model of the mechanism of ATP-driven uneven protein distribution pattern formation along a DNA molecule. The structure of the helical MuB polymer is studied by EM image reconstruction. The reaction system studied here is an example of simple biomolecular patterning reactions, and the experimental techniques developed here will be exploited for parallel studies of mechanistically related reaction systems.